Conductive interconnect structures incorporating negative thermal expansion materials and associated systems, devices, and methods

ABSTRACT

Semiconductor devices having interconnects incorporating negative expansion (NTE) materials are disclosed herein. In one embodiment a semiconductor device includes a substrate having an opening that extends at least partially through the substrate. A conductive material having a positive coefficient of thermal expansion (CTE) partially fills the opening. A negative thermal expansion (NTE) having a negative CTE also partially fills the opening. In one embodiment, the conductive material includes copper and the NTE material includes zirconium tungstate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/889,120, filed Feb. 5, 2018, now U.S. Pat. No. 10,546,777; which is acontinuation of U.S. application Ser. No. 15/653,365, filed Jul. 18,2017, now U.S. Pat. No. 9,922,875; which is a continuation of U.S.application Ser. No. 14/815,560, filed Jul. 31, 2015, now U.S. Pat. No.9,754,825; which is a divisional of U.S. application Ser. No.13/959,429, filed Aug. 5, 2013, now U.S. Pat. No. 9,099,442; each ofwhich is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The present technology is related to semiconductor device interconnects,such as vias, traces, and other contact structures that includematerials that have a negative coefficient of thermal expansion (CTE).

BACKGROUND

Forming semiconductor devices typically includes subjecting asemiconductor substrate or assembly to a series of processing steps foradding, removing, and/or altering material. Cumulatively, theseprocessing steps can precisely form very high densities of electricalcomponents, e.g., transistors, capacitors, and diodes. The electricalcomponents can be connected by complex network connections thattypically extend over and through multiple layers. Such networkconnections from one layer to another layer can be vias formed byselectively etching holes through semiconductor materials in desiredpatterns and filling the holes with a conductive material. Athrough-silicon via (TSV) is one type of via that extends through theentirety of a semiconductor substrate. The TSV is isolated from thesubstrate by a dielectric spacer and electrically intercouples contactsor other conductive features at opposite sides of the substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a cross-sectional side view of a semiconductor device havinga TSV configured in accordance with an embodiment of the presenttechnology.

FIGS. 1B and 1C are cross-sectional top views of the TSV of FIG. 1A atan initial temperature level and at an elevated temperature level,respectively, in accordance with an embodiment of the presenttechnology.

FIGS. 2A-2C are cross-sectional side views showing TSVs with differentvolumetric ratios of negative thermal expansion materials configured inaccordance with selected embodiments of the present technology.

FIGS. 3A-3E are cross-sectional views illustrating the semiconductordevice of FIG. 1A at selected steps in a method of manufacture inaccordance with selected embodiments of the present technology.

FIGS. 4A and 4B are cross-sectional side views of a semiconductor devicehaving a TSV configured in accordance with another embodiment of thepresent technology.

FIGS. 5A-5C are isometric views of interconnect structures configured inaccordance with other embodiments of the present technology.

FIG. 6 is a block diagram illustrating a system that incorporates asemiconductor device in accordance with an embodiment of the presenttechnology.

DETAILED DESCRIPTION

Specific details of several embodiments of the present technology relateto electrodes in semiconductor devices incorporating negative thermalexpansion (NTE) materials. The term “semiconductor device” generallyrefers to a solid-state device that includes semiconductor materials.Semiconductor devices can be logic devices, memory devices, and diodes,among others. Semiconductor devices can also include light emittingsemiconductor devices, such as light emitting diodes (LEDs), laserdiodes, and other solid state transducer devices. Further, the term“semiconductor device” can refer to a finished device or to an assemblyor other structure at various stages of processing before becoming afinished device. The term “interconnect” can refer to any of a varietyof conductive structures that extend vertically through and/or laterallyacross a portion of a semiconductor device or substrate. Examples ofinterconnects include vias, traces, contact pads, wires, and otherconductive structures. Depending upon the context in which it is used,the term “substrate” can refer to a wafer-level substrate and/or to asingulated, die-level substrate. In addition, unless the contextindicates otherwise, structures disclosed herein can be formed usingconventional semiconductor-manufacturing techniques. Materials can bedeposited, for example, using chemical vapor deposition, physical vapordeposition, atomic layer deposition, spin coating, and/or other suitabletechniques. Similarly, materials can be removed, for example, usingplasma etching, wet etching, chemical-mechanical planarization (CMP), orother suitable techniques. Also, materials can be patterned, forexample, by adding and/or removing materials using one or more maskmaterials, such as photoresist materials, hard-mask materials, or othersuitable materials.

One problem with conventional interconnect materials (e.g., metallicmaterials) is that they expand and contract more than many othermaterials in the substrate in response to temperature changes occurringin many of the manufacturing processes and operation. In general,interconnects expand in size based on their volume and coefficient ofthermal expansion (CTE), and typically, the CTE of many interconnectmaterials is significantly larger than the CTE of materials in thesubstrate. For example, copper can have a CTE of about 1.7×10⁻⁵ l/K(linear), whereas silicon can have a CTE of about 2.3×10⁻⁶ l/K (linear).At elevated temperatures, this disparity in CTE causes the interconnectsto expand to a greater extent than adjacent substrate materials. Thisexpansion imposes a stress on the surrounding materials and leads tocracks in the substrate. These cracks can ultimately result in waferbreakage, device malfunction due to silicon lattice damage, devicefailure, and yield loss. Interconnects configured in accordance withseveral embodiments of the present technology, however, address theseand other limitations of conventional interconnects.

FIG. 1A is a cross-sectional side view of a semiconductor device 100configured in accordance with an embodiment of the present technology.The semiconductor device 100 includes a substrate 102 and an electricalcomponent 103 (shown schematically). The substrate 102 can include, forexample, a silicon substrate, an epitaxial structure, a stack ofsemiconductor materials, or other suitable structures. The electricalcomponent 103 can be, for example, a transistor, a diode, an LED, acapacitor, an integrated circuit, etc.

The semiconductor device 100 further includes a network of conductiveinterconnects 105 configured to route electrical signals to internalcomponents (e.g., the electrical component 103) and/or to externalcomponents (e.g., off-chip components). The interconnects 105 caninclude, for example, a via 106, a contact structure 108, and a trace109 connecting the via 106 with the contact structure 108. In one aspectof the embodiment of FIG. 1A, the interconnects 105 also include a TSV110 formed in a through hole 112 that extends through the substrate 102between a first side 113 a (e.g., a top or active side) and a secondside 113 b (e.g., a bottom or back side). As shown, the TSV 110 isisolated from the substrate 102 by a spacer material (not visible inFIG. 1A) and includes at least one outer conductive material 115 and atleast one NTE material 116. The outer material includes a positive CTEmaterial, such as aluminum, copper, silver, platinum, ruthenium,titanium, cobalt, etc. The NTE material 116, on the other hand, includesa negative CTE material. In one embodiment, the NTE material 116 caninclude a metal-oxide crystalline material. For example, zirconiumtungstate (Zr(WO₄)₂) is one such material that has a negative CTE ofapproximately −4.9×10⁻⁶ l/K. Unlike most crystalline materials,zirconium tungstate has “flexibly-hinged” lattice components (ZrO₆ andWO₄) that respond to increases in heat by reordering and/or rotatingthemselves into more compact configurations within the lattice. OtherNTE materials can have lattice components that exhibit similarmechanisms of contraction when heated. For example, ZrW₂O₈ is acrystalline material that can have a negative CTE of approximately−11.4×10⁻⁶ l/K.

As used herein, the term “NTE material” refers to a material thatcontracts in volume in response to an increase in temperature. Similarto a positive CTE material, an NTE material has a CTE associated withits magnitude of expansion/contraction over certain ranges temperature.However, unlike a positive CTE material, an NTE material has a negativeCTE over certain temperature rages (e.g., −50° C. to 250° C.). Othermaterial properties, features, and compositions associated with NTEmaterials are described, for example, in T. A. Mary et al. “NegativeThermal Expansion from 0.3 to 1050 Kelvin in ZrW₂O₈.” Science 272.5258(1996): 90-92; D. Keen et al. “Negative thermal expansion in zirconiumtungstate.” Phys. Rev. Lett. 96 (2005); H. Liu et al. “Effect ofpost-deposition annealing on ZrW₂O₈ thin films prepared by radiofrequency magnetron sputtering.” Surface and Coatings Technology.201.9-11 (2007):5560-5563; M. S. Sutton et al. “Deposition dependence ofzirconium tungstate (ZrW₂O₈) based negative thermal expansion films foroptical coatings.” Optical Interference Coatings (OIC) Tucson, Ariz.,Jun. 27, 2004, Deposition of Optical Coatings III (ME); S. Singamaneniet al. “Negative Thermal Expansion in Ultrathin Plasma.” PolymerizedFilm Chm. Mater. 19 (2007): 129-131; Cora Lind. “Two Decades of NegativeThermal Expansion Research: Where Do We Stand?” Materials 2012, 5,1125-1154; W. Sleight. “Negative Thermal Expansion.” Mat. Res. Soc.Symp. Proc. Vol. 755 2003 Materials Research Society.

FIG. 1B is a cross-sectional top view of the TSV 110 at an initialtemperature level T₁ (e.g., room temperature), and FIG. 1C shows the TSV110 at an elevated temperature level T₂ (e.g., a manufacturing oroperating temperature) in accordance with an embodiment of the presenttechnology. At the initial temperature level T₁ (FIG. 1B), theconductive material 115 and the NTE material 116 interface with oneanother at a first circumference level C₁. At the elevated temperaturelevel T₂ (FIG. 1C), the conductive material 115 has expanded and the NTEmaterial 116 has contracted to expose an open space). As a result, aportion of the conductive material 115 can expand into the open space torelax the stress caused by thermal expansion.

Although not visible in FIG. 1C, the conductive material 115 can expandin the vertical direction (i.e., into the plane of the page) and the NTEmaterial 116 can contract in the vertical direction between the firstand second sides 113 a and 113 b (FIG. 1A). In general, theexpansion/contraction in the vertical direction does not cause thetypical (substrate) cracking, and the other types of damage associatedwith the conventional lateral expansion/contraction discussed above. Insome embodiments, the expansion/contraction in the vertical directioncan produce an open space at either ends of the TSV 100 (similar to theopen space that be produced due to expansion/contraction in the lateraldirection).

The change in volume of the NTE material 116 can be based, at least inpart, on its negative CTE value, initial volume, and the change intemperature (i.e., T₂−T₁). In one embodiment, a change in the volume ofthe NTE material, ΔV_(NTE), can be approximated by Equation 1, asfollows:ΔN _(NTE)=α₁ ×V _(NTE)(T ₂ −T ₁)  (1)where α₁ represents the negative CTE of the NTE material 116 and V_(NTE)represent the initial volume of the NTE material 116 at the initialtemperature level T₁.

The change in the outer volume of the conductive material 115 is based,at least in part, on its positive CTE value, initial volume, and thechange in temperature. In one embodiment, the change in the volume ofthe outer material, ΔVo, can be approximated by Equation 2, as follows:ΔVo=α ₂ ×Vo(T ₂ −T ₁)  (2)where α₂ represents the positive CTE of the conductive material 115 andVo represents the initial volume of the conductive material 115 at theinitial temperature level T₁.

In accordance with various embodiments of the present technology, theTSV 110 can have a composite CTE that is based, at least in part, on theCTE of each material in the TSV 110 as well as the volume of eachmaterial in the TSV 110. In one embodiment, a composite CTE, α_(c), canbe approximated by Equation 3, as follows:α_(c)=β×α₁ ×V _(NTE)(1−β)×α₂ ×Vo  (3)where β is a volumetric ratio associated with the NTE material 116. Thevolumetric ratio β can be approximated by Equation 4, as follows:β=V _(NTE) /V _(T)  (4)where V_(T) is the total volume of the TSV 110 (i.e., the aggregate ofthe volume of each material in the TSV 110).

In some embodiments, a composite CTE can be customized or engineered tohave a particular value by selecting certain types of conductivematerials and/or NTE materials. For example, when the conductivematerial 115 is composed of gold in lieu of copper, the composite CTEhas a lesser value because gold has a lower CTE than copper. Asdescribed below, another way to configure the composite CTE is to changethe volumetric ratio β associated with the NTE material 116.

FIGS. 2A-2C are cross-sectional side views showing TSVs 210 (identifiedindividually as first through third TSVs 210 a-210 c) with differentvolumetric ratios β of the NTE material 116 in accordance with selectedembodiments of the present technology. Referring first to FIG. 2A, afirst volumetric ratio β₁ provides a composite CTE having a value ofzero (α_(c)=0). In FIG. 2B, a second volumetric ratio β₂ (<β₁) providesa composite CTE having a positive value (α_(c)>0). In FIG. 2C, a thirdvolumetric ratio β₃ (>β₁) provides a composite CTE having a negativevalue (α_(c)<0).

Referring to FIGS. 2A-2C together, when heated, the first TSV 210 a canexpand or contract in proportion to its composite CTE. For example, whenit has the first volumetric ratio β₁ (i.e., when α_(c)=0), the first TSV210 a will not substantially expand or contract when heated. However,with the second volumetric ratio (32 (i.e., when α_(c)<0), the secondTSV 210 b will generally expand when heated, albeit less than theexpansion of a volume of the conductive material 115 alone. On the otherhand, with the third volumetric ratio β₃ (i.e., when α_(c)<0), the thirdTSV 210 c contracts when heated. In some configurations, the third TSV210 c can contract at the same ratio at which another material expands.For example, the third TSV 210 c can contract at the same ratio at whichthe adjacent substrate 102 expands.

FIGS. 3A-3E are cross-sectional views illustrating the semiconductordevice 100 at selected steps in a method of manufacture in accordancewith selected embodiments of the present technology. As shown in FIG.3A, a dielectric material 321 (e.g., oxide, silicon carbide, siliconnitride, etc.) has been formed on the substrate 102, and an opening 320has been formed through the first side 113 a of the substrate 102 andthe dielectric material 321. In some embodiments, the dielectricmaterial 321 can be employed as a stopping material in a CMP processduring TSV isolation. The opening 320 includes a recessed surface 322and sidewalls 323 extending to an intermediate depth within, but notcompletely through, the substrate 102. In the illustrated embodiment,the opening 320 has a circular (or ovular) shape (viewed from, e.g., thefirst side 113 a of the semiconductor device 100). In other embodiments,however, the opening 320 can have a different configuration. Forexample, the opening 320 can be a trench. FIG. 3B shows thesemiconductor device 100 after a dielectric liner 324 (e.g., an oxideliner) and a conductive material 315 have been formed, respectively, inthe opening 320. In the illustrated embodiment, the conductive material315 toward the bottom of the opening 320 is thicker than the conductivematerial toward the sidewalls in the opening 320. In one embodiment, abottom-up plating process can be used to form relatively thicker metal(e.g., copper) at the bottom of the opening followed by more uniformplating along the sidewalls once the thicker metal has been formed. Theconductive material 315 can include, for example, copper, tungsten,gold, silver, platinum, aluminum, etc. In some embodiments, theconductive material 315 is an electroplated material that lines therecessed surface 322, the side walls 323, and an outer surface 325 ofthe substrate 102. The semiconductor device 100 can also include abarrier and/or seed materials 327 between the conductive material 315and portions of the substrate 102. The barrier and/or seed materials 327can include, for example, tantalum, tantalum nitride, tungsten,ruthenium, copper, titanium, titanium nitride, or other suitablematerials.

FIG. 3C shows the semiconductor device 100 after an NTE material 316 hasbeen deposited on the conductive material 315. The NTE material 316 canbe deposited, for example, using chemical vapor deposition or othersuitable techniques. As discussed above, the NTE material 316 caninclude a metal oxide such as zirconium tungstate. Another suitable NTEmaterial can include ZrV₂O₇. In other embodiments, suitable NTEmaterials can include members of the ‘A’ ‘M’₂O₈ family of compoundsand/or the ‘A’₂(‘M’O₄)₃ family of compounds, where ‘A’ can includezirconium or hafnium and ‘B’ can include molybdenum or tungsten.

FIG. 3D shows the semiconductor device 100 after forming other devicefeatures. In the illustrated embodiment, an additional conductivematerial 329 forms an interconnect structure that connects theconductive material 315 with the contact 106. As shown, an additionaldielectric material 311 has been formed on the dielectric material 321and the NTE material 316, a portion of the dielectric material has beenremoved (e.g., etched) to form openings in the dielectric materials 311,321, and the openings formed in the dielectric materials 311, 321 havebeen filled with portions of the conductive material 329. In someembodiments, the conductive material 329 can be deposited on at least aportion of the NTE material 316 at the first side 113 a.

FIG. 3E shows the semiconductor device 100 after removing portions ofthe conductive material 315 and the substrate 102 to expose portions ofthe conductive material 315 at the second side 113 b. Material can beremoved by, for example, backgrinding, etching, CMP and/or othersuitable removal methods. Also, various passivation materials (not shownin FIG. 3E) can be employed at the second side 113 b to protect thesubstrate 102 and prevent contamination (e.g., metallic contamination).In one embodiment, a thinning process may use exposure of the dielectricmaterial of the liner 324 at the second side 113 b (to detect when theremoval process should be stopped, such as an endpoint detection, toenhance process control in subsequent processing. In another embodiment,conductive materials (e.g., the conductive material 315 and/or thebarrier seed materials 327) can provide endpoint detection. Afterexposing portions of the conductive material 315, processing cancontinue, for example, to form other features (e.g., the contactstructure 108 (FIG. 1A) as well as to device singulation, testing,and/or packaging.

FIG. 4A shows a TSV 410 including the conductive material 315 and theNTE material 316 (e.g., after the stage of FIG. 3D) after the substrate102 has been thinned to expose the dielectric liner 324 at the secondside 113 b such that portions of the dielectric liner 324 and theconductive material 315 project beyond the substrate material at thesecond side 113 b. A dielectric material 417 is then formed at thesecond side 113 b. The dielectric material 417 can be a conformal ornon-conformal material, including a low-temperature dielectric thatinitially covers the TSV 410 at the second side 113 b. A subsequentmaterial removal process (having a higher controllability) can exposethe conductive material 315 (or, alternatively, the conductive material315 along with a portion of the NTE material 316) by removing portionsof the thick dielectric material 417 and the dielectric liner 324.

FIG. 4B shows a thick dielectric material 440 (e.g., low temperatureoxide, nitride, carbide, etc.) that is deposited on the dielectricmaterial 417 and the exposed conductive material 315 of FIG. 4A. In theillustrated embodiment, an additional conductive material 419 can forman electrical contact. For example, the thick dielectric material 440and the conductive material 419 can form a damascene structure.

FIGS. 5A-5C are isometric views of interconnect structures configured inaccordance with other embodiments of the present technology. Similar tothe TSVs discussed above, the interconnect structures of FIGS. 5A-5C canbe configured to incorporate NTE materials. FIG. 5A is an example thatshows a conductive trace 530 a that includes an outer conductivematerial 515 a arranged in parallel lines 532 and an inner NTE material516 a between the parallel lines 532. FIG. 5B shows an example of acontact pad 530 b having an outer conductive material 515 b arranged ina square pattern 533 and an inner NTE material 516 b in the center ofthe square 533. Figure K is an example of an interlevel dielectric 535having an outer dielectric material 517 (e.g., an oxide) and an innerNTE material 516 c configured as a via 530 c. Unlike the TSVs discussedabove, the via 530 c does not include an outer conductive material. Inone embodiment, the NTE material 516 c is configured such that atelevated temperatures the NTE material 516 c contracts at the same ratioat which the outer dielectric material 517 expands (and vice versa).

Any one of the semiconductor devices having the features described abovewith reference to FIGS. 1A-5 can be incorporated into any of a myriad oflarger and/or more complex systems, a representative example of which issystem 690 shown schematically in FIG. 6. The system 690 can include aprocessor 692, a memory 694 (e.g., SRAM, DRAM, flash, and/or othermemory devices), input/output devices 696, and/or other subsystems orcomponents 698. The semiconductor assemblies, devices, and devicepackages described above with reference to FIGS. 1A-5C can be includedin any of the elements shown in FIG. 6. The resulting system 690 can beconfigured to perform any of a wide variety of suitable computing,processing, storage, sensing, imaging, and/or other functions.Accordingly, representative examples of the system 690 include, withoutlimitation, computers and/or other data processors, such as desktopcomputers, laptop computers, Internet appliances, hand-held devices(e.g., palm-top computers, wearable computers, cellular or mobilephones, personal digital assistants, music players, etc.), tablets,multi-processor systems, processor-based or programmable consumerelectronics, network computers, and minicomputers. Additionalrepresentative examples of the system 690 include lights, cameras,vehicles, etc. With regard to these and other examples, the system 690can be housed in a single unit or distributed over multipleinterconnected units, e.g., through a communication network. Thecomponents of the system 690 can accordingly include local and/or remotememory storage devices and any of a wide variety of suitablecomputer-readable media.

From the foregoing, it will be appreciated that specific embodiments ofthe present technology have been described herein for purposes ofillustration, but that various modifications may be made withoutdeviating from the disclosure. In various embodiments, theabove-described interconnects can vary in shape, size, number, and othercharacteristics. For example, the NTE material 116 (FIG. 1) can beformed such that a gap or void is incorporated (or naturally occurs)within the center of the TSV 100 (FIG. 1). Also, in some embodiments,the NTE 116 material can be deposited such that it covers orencapsulates the conductive material 115 (FIG. 1). For example, in someembodiments, the conductive material 115 can form the interior portionof the TSV 100 and the NTE material 116 can be employed as a cappingmaterial. In addition, certain aspects of the disclosure described inthe context of particular embodiments may be combined or eliminated inother embodiments. Further, while advantages associated with certainembodiments have been described in the context of those embodiments,other embodiments may also exhibit such advantages. Not all embodimentsneed necessarily exhibit such advantages to fall within the scope of thepresent disclosure. Accordingly, the disclosure and associatedtechnology can encompass other embodiments not expressly shown ordescribed herein.

We claim:
 1. A semiconductor device, comprising: a substrate; aconductive structure disposed over the substrate, the conductivestructure including: an inner material having a negative coefficient ofthermal expansion (CTE), and an outer material disposed adjacent to andlaterally outward from the inner material, the outer material having apositive CTE.
 2. The semiconductor device of claim 1, wherein theconductive structure is a trace.
 3. The semiconductor device of claim 2,wherein the inner material is a conductive material arranged in a line,and wherein the outer material is disposed adjacent to and laterallyoutward from the line.
 4. The semiconductor device of claim 2, whereinthe outer material is a conductive material arranged in parallel lines,and wherein the inner material is disposed between and laterally inwardfrom the parallel lines.
 5. The semiconductor device of claim 1, whereinthe outer material is disposed on opposing lateral sides of the innermaterial.
 6. The semiconductor device of claim 1, wherein the conductivestructure is an interconnect structure.
 7. The semiconductor device ofclaim 6, wherein the interconnect structure is a contact pad.
 8. Thesemiconductor device of claim 1 wherein the inner material includesZr(WO₄)₂, ZrV₂O, ZrMo₂O₈, ZrW₂O₈, HfMo₂O₈, or HfW₂O₈, Zr₂(MoO₄)₃,Zr₂(WO₄)₃, Hf₂(MoO₄)₃, Hf₂(WO₄)₃, or a combination thereof.
 9. Thesemiconductor device of claim 1 wherein the conductive structure isconfigured so that at a first temperature, the inner material contractsat a same ratio at which the outer material expands.
 10. Thesemiconductor device of claim 1 wherein the conductive structure isconfigured so that at a second temperature, the inner material expandsat a same ratio at which the outer material contracts.
 11. Thesemiconductor device of claim 1 wherein the inner and outer materialstogether have a composite CTE that is less than the positive CTE, butgreater than the negative CTE.
 12. The semiconductor device of claim 11wherein the composite CTE is less than zero.
 13. The semiconductordevice of claim 11 wherein the composite CTE is equal to about zero. 14.A method of manufacturing a semiconductor device, comprising: disposingan inner material over a substrate, wherein the inner material has anegative coefficient of thermal expansion (CTE); and disposing an outermaterial over the substrate, adjacent to and laterally outward from theinner material, wherein the outer material has a positive CTE.
 15. Themethod of claim 14 wherein the outer material is disposed on opposingsides of the inner material.
 16. The method of claim 14 wherein theouter material is a conductive material arranged in parallel lines, andwherein the inner material is between and laterally inward from theparallel lines.
 17. The method of claim 14 wherein the inner materialincludes Zr(WO₄)₂, ZrV₂O, ZrMo₂O₈, ZrW₂O₈, HfMo₂O₈, or HfW₂O₈,Zr₂(MoO₄)₃, Zr₂(WO₄)₃, Hf₂(MoO₄)₃, Hf₂(WO₄)₃, or a combination thereof.18. The method of claim 14 wherein at a first temperature, the innermaterial contracts at a same ratio at which the outer material expands.19. The method of claim 14 wherein at a second temperature, the innermaterial expands at a same ratio at which the outer material contracts.20. The method of claim 14 wherein the inner and outer materialstogether have a composite CTE that is less than the positive CTE, butgreater than the negative CTE.
 21. The method of claim 20 wherein thecomposite CTE is less than zero.
 22. The method of claim 20 wherein thecomposite CTE is equal to about zero.